The present invention relates to an image outputting apparatus for printing an image as an array of points, (pixels), such as a printer and a facsimile, and, more particularly, the invention relates to a unit for processing an image by effecting continuous gradation by combining laser pulse width modulation (PWM) and a plurality of pixels.
Hitherto, a halftoning method, known as a dither method or an error diffusion method, has been used in a raster device, in which a pixel has a two-value (binary) output such as a digital printer and the like.
Among known dither methods in particular, there is a halftoning method called a dot concentrated dither method by means of which a threshold pattern as shown in FIG. 3b of Japanese Patent Laid-Open No. 61-125264 has been used. This method simulates halftone dots whose diameter changes corresponding to an inputted gradation by using a plurality of pixel arrays. This method has an advantage in that noise mixed into an image to be reproduced by the halftoning is not noticeable. This method also make it possible to reconcile the density of halftone dots and a number of gradations by using a sub-matrix method, as shown in FIG. 17a of Japanese Patent Laid-Open No. 61-125264, in which threshold pattern is constructed by a few halftone dots (dither) pattern which expand one after another.
A similar halftoning is also seen in FIG. 21(B) of Japanese Patent Publication No. 6-85558. Japanese Patent Publication No. 6-85558 in particular has a three-value output pixel produced by pulse width modulation (PWM) of an output laser. Then, this halftoning method adopts a procedure for determining a three-value output level by using in combination another threshold array shown in FIG. 21(A) corresponding to one shown in FIG. 21(B).
While those methods have been devised in order to reconcile the number of gradations and the resolution, they are not always enough for a laser printer of 600 dpi (dots per inch) It is required to have a density of 175 lpi of halftone dots and 256 gradations in order to reproduce an image in the level of gravure. Here, the unit "lpi" is a density of halftone dots per inch (lines per inch). "lpi" is discriminated from "dpi", i.e., the resolution of the printer engine itself.
It is impossible for a printer of around two-value and 600 dpi to create halftone dots of such a density of gradation. However, a visually discriminable number of gradations depends on the spatial frequency, and no such number of gradations is required for a high-frequency component.
According to P. Roetling, "Visual Performance and Image Coding", SPIE/OSA Vol. 74 on Image Processing, 1976, pp. 195-199, a discriminable number of gradations Gn with respect to a spatial frequency f (cycles/degree) maybe modeled by the following expression: EQU Gn=1010(exp(-0.138f))(1-exp(-0.1f))+1 (1)
FIG. 21 shows visual characteristics of the discriminable number of gradations in correspondence with resolution of a printer based on the expression. Solid lines in the graph indicate the discriminable number of gradations with respect to the spatial frequency according to the expression (1) Broken lines indicate the number of gradations which can be realized by the printer of n-value and 600 dpi. In FIG. 21, particular, the spatial frequency is shown by converting into a density of halftone dots at an observation distance of 30 cm and 40 cm, respectively. 1 (cycle/degree) corresponds to about 10 (lpi) at the observation distance of 30 cm.
The portion where the broken lines exceed the solid lines indicates that enough gradation can be obtained with respect to the spatial frequency. Accordingly, it can be seen from this graph that at least one dot must be a five to nine-value in order to obtain a fully smooth gradation by a printer having a resolution of 600 dpi.
Meanwhile, one halftone dot must be composed of a set of 3.times.3 pixels or less in order to create halftone dots of 175 lpi by a printer with a resolution of 600 dpi. The number of gradations at this time is 3.times.3.times.9+1=82 even by a nine-value printer, so that the number of gradations in the low frequency range is not sufficient. Therefore, it is impossible to obtain a sufficient gradation only by the clustering method (sub-matrix method) Further, a number of divisions of PWM cannot be increased so much to obtain the gradation only by PWM because it requires a control circuit of higher frequency at the same printing speed, thus causing a problem in increasing the speed and in terms of the packaging cost.
Therefore, it becomes necessary to use the clustering method as shown in the above-mentioned Japanese Patent Laid-Open No. 61-125246 and PWM in combination.
Further, there has been a problem that a threshold array and a comparator become large in a nine-value printer by the method of providing the threshold array corresponding to respective concentration levels of 1/3 and 2/3 of the dot concentration as shown in Japanese Patent Publication No. 6-85558.
The increase of the scale of the circuit structure and the required memory for such a method increases not only the cost, but also the burden, in developing a dedicated LSI (ASIC) for the process.